arXiv:2608.31126math.NT
Polymath8b proved that $H_1 = \liminf (p_{n+1}-p_n) \leq 246$. In this paper we show how the Bombieri-Vinogradov theorem can be combined with newer equidistribution estimates for smooth moduli to obtain the improved bound $H_1 \leq 240$.
Linked by 3 identifiable commenters in 3 comments across 3 threads, from Sep 2026 to Sep 2026. Found in 1 HN submission from Sep 2026 to Sep 2026. Open submission discussions.
Context - according to Wikipedia [0], just a few days ago someone posted a proof of a bound of 240 [1]. [0] https://en.wikipedia.org/wiki/Twin_prime [1] https://arxiv.org/abs/2608.31126
Just two days ago, a preprint by Julia Stadlmann went up on arXiv [0] improving the prime gap from 246 to 240. Now OpenAI announces Astra has shown a gap of 186 [1]. That must really blow. [0] https://arxiv.org/abs/2608.31126 [1]…
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Reminds me, kinda, to when Astra was launched and OpenAI announced an improvement to the bounded prime gap. Which BTW, Prof. Julia Stadlmann had published an independent result only a few days earlier Stadlmann improved it from 246 to 240, OpenAI later claimed 186 I think? Maybe…
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